Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks

摘要

The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed system of integral differential equations and a nonlinear scalar integral differential equation.It will be shown that there exist six standing wave solutions ((u(x,t),w(x,t)) =(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations.Similarly,there exist six standing wave solutions u(x,t) =U(x) to the nonlinear scalar integral differential equation.The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.